España 
Italia 
United States 
Brasil 
Chile
Ecuador
Mexico
Colombia
Perú
sdds NCSM (National Council of Supervisors of Mathematics) i l’NCTM (National Council of Teachers of Mathematics). La primera, pensada per a equips directius i responsables educatius; la segona, per a mestres i docents.
These conferences are a wonderful opportunity to connect with professionals from around the world, share experiences, and gather a host of ideas to keep improving how we teach and learn mathematics. We were also fortunate to participate with our own talks, activities, and workshops.
This year we ran activities intensively at the booth! In this article we want to share the experience and explain what we discovered so that you can take away ideas and recommendations about trends in math education.
What are NCSM and NCTM?
Every year, during a week in October, these two reference conferences take place in the United States. NCTM, founded in 1920, is the main U.S. organization dedicated to improving the teaching and learning of mathematics. NCSM, for its part, focuses on leadership and educational supervision, offering a meeting space for directors, trainers, and program leaders.
Both institutions organize annual conferences. Although each has its own focus, they share the same mission: to promote mathematics education that is more meaningful, equitable, and connected to real life.
Atlanta, host city
This year, Atlanta (Georgia), known as the City in the Forest for its lush green surroundings, hosted these two major events. In a warm and welcoming climate, we enjoyed days full of great ideas, mathematical challenges, and inspiring meetings.
As a curiosity, Atlanta is home to the world’s busiest airport, Hartsfield–Jackson — with more than 100 million passengers a year! A fact sure to delight fans of large numbers.
Thinking and doing math!
Several members of Innovamat’s teaching team traveled to Atlanta to invite teachers to do what we love most: think mathematically! At the Innovamat space, hundreds of teachers came by to solve challenges, experiment with vertical whiteboards, and share strategies.
And true to our word: now we’ll make you think! One of the activities we proposed was this productive-practice task for everyone else:
Fill the hives with numbers from 1 to 6 following these conditions:
- In each cell there must be the difference between the numbers in the two cells below it.
- Numbers cannot be repeated within each bee.
We encourage you to grab paper and pen and start placing the numbers in the different cells! You’ll begin to find patterns and eliminate numbers for certain cells. And one thing is certain: you’ll do many more subtractions than with a traditional worksheet. That’s why research calls it productive practice—because the task leads us to “produce” operations, do more calculations, and develop fluency.
If you’ve tried the exercise, we encourage you to share it on social media and tag us! And the big question: Can you guarantee that there’s only one solution?
Special moments and encounters
We proposed other rich tasks, such as the reminders race or multiplicative persistence, and we saw teachers and trainers enjoying themselves like children, searching for patterns and arguing ideas.
We also received very special visits: figures like Pam Harris, Kim Montague, Kourtney Peters, Grace Kelemanik, and Dan Meyer stopped by to solve the activities! In fact, Pam and Dan stayed for a long time when they realized there wasn’t a single solution.
It’s very comfortable living by running activities! Peter Liljedahl came by for a visit and proposed this problem, which we invite you to solve:
How many upward-pointing triangles would you be able to find? How sure can you be that you have found them all? What was your strategy?
Time to think! We had a great moment with Imelda and Ricard being exhaustive!
And one last curiosity, observed by the ever-attentive Albert Vilalta: our booth number was, no more and no less, 1433. A prime number!
The ideas we take away
Members of Innovamat’s teaching team habitually attend every possible mathematics education conference to continue training ourselves and build community with teachers. For NCTM, you can consult the chronicles from previous years:
This year, the talks and workshops revolved around seven big ideas that shape the current direction of math education:
Pam Harris — Avoiding the trap of algorithms and developing mathematical thinking
Pam Harris insisted that the most important thing is to do mathematics: activate prior knowledge (“known facts”) and deduce new facts through different strategies, which we refer to as “known facts–derived facts.” She showed many examples while projecting her tablet and capturing in a different color the reasoning of participants to make thinking visible and legitimize all strategies.
The underlying message: to formalize, you first need to deeply understand a concept and live the experience of thinking.. All these ideas are collected in the book Developing Mathematical Reasoning: Avoiding the Trap of Algorithms.
Peter Liljedahl — The Explore–Explain and Thin-Slicing
Peter Liljedahl, author of the well-known Building Thinking Classrooms, emphasized in the talk “Seeing and Being Seen in Math Class” the importance of students feeling seen and recognized by teachers and peers. Based on Bandura’s self-efficacy theory, he showed how thinking tasks, visible random groups, and vertical surfaces foster a classroom where everyone can learn from others and feel competent.
In his second talk, Thin-Slicing 101: A Deep Dive into the Heart of Building Thinking Classrooms Liljedahl va aprofundir en el thin slicing, estratègia que divideix les tasques en petits reptes per mantenir el flow —the balance between a student disengaging from boredom and disengaging from frustration—and adapt to all learners. He emphasized the importance of planning tasks and opening the classroom to conversations about errors.
Graham Fletcher — Pull Up a Chair: assessing to grow thinking
Assessment is “pulling up a chair”: listening with intent and building on students’ strengths. Graham Fletcher advocates an asset-based view rather than a deficit view, and the use of progressions to understand where each student is and where they can go. Assessment thus becomes a tool for dialogue and growth, where we view each student’s learning from abundance rather than lack.
Bay-Williams — Fluency with meaning: strategies before memory
A session focused on basic facts and fluency with meaning. The key: teach reasoning strategies to all students, with explicit instruction of strategies (not traditional direct instruction). Visuals, contexts, and relationships help show how, why, and when a strategy works. One idea we liked was thinking in terms of acceleration. Acceleration doesn’t mean going faster; it means thinking more deeply and making connections.
Mike Flynn — The future of teacher learning: intersynchronous, relevant, and human
Mike Flynn immersed us in a session on new formats for teacher professional learning. He proposed many flexible, connected, and relevant ideas and experiences, closely related to audiovisual content and real classroom recordings. We left with many references! The idea is to embrace intersynchronous formats (a combination of live sessions and on-demand resources) and training formats that are more active, brief, and personalized so teachers can extract ideas and good practices in a connected and applied way.
Dan Meyer — The gifts (or takings) technology can bring to the math classroom
Dan Meyer focused his talk on how, despite its potential, much educational technology in math can work against a truly participatory and effective classroom.. He identified three “gifts” that technology has given our daily lives—connection, creativity, and real-time feedback—and showed how these are often lost when we transfer digital tools to the classroom. Dan urged teachers to reclaim those three elements by using technology to connect students, foster creativity, and provide meaningful feedback.
Catherine Fosnot — The link between research and practice
She went deeper into what it means for math materials to be research-based, highlighting four pillars: evidence-based learning trajectories, sequences of tasks with low entry and high ceiling, use of meaningful contexts to foster engagement and mathematical identity, and teacher learning tied to the materials to ensure real systemic change. Examples and research data presented showed significant improvements in both teacher development and student performance in participating districts.
Jo Boaler & Cathy Williams — Identity and agency through data
They presented the Women in Data Science movement and the book Data Minds, with a clear message: data competence is crucial for participating in today’s society. We should teach data not just to describe the world but to understand it, protect ourselves, and transform it.. They shared inspiring ideas for fostering creativity and critical awareness through data science.
Toni Galassini & Carrie Cutler — From Color Tiles to Cuisenaire Rods: Building Reasoning in PreK–2
A lovely early childhood session! Toni Galassini and Carrie Cutler showed how manipulatives (such as color tiles, Cuisenaire rods, or two-color counters) can be bridges to abstract thinking.. These tools encourageexperimentation, visualization, pattern recognition, communication, and logical reasoning.. They shared games like Shake and Spill, Trains to 12, and Fill the Hexagon, which demonstrate that manipulatives are not just an initial phase but a way to build meaning and deep connections starting in early childhood. You can find the resources they shared here. here.
Our contributions
At both NCTM and NCSM, several members of Innovamat’s teaching team had the opportunity to present workshops and talks with the participation of Pam Brett, Rob Baier, Nolan Fossum, Manuel Méndez, Albert Vilalta, Judith Fàbrega, and Laura Morera.
Thanks to everyone who attended and shared this space with us!
A conference to learn and inspire
Each session, each conversation, and each shared challenge reminded us why we do what we do: because mathematics is much more than numbers—it’s a way of thinking, communicating, and understanding the world.
In Atlanta we confirmed, once again, that learning mathematics is learning to be curious, persistent, and human.
And we’re already counting the days until we meet again at the next teaching conference!
